Saying that gay couples are equal to straight couples is essentially a religious argument because it places value on behavior, something that government should not be involved in.
If the government is going to enforce (legally) this equality, then they are becoming a state-run religion and trampling on my (and a bunch of other people's) freedom of religion.
The argument should completely avoid assigning value to a gay relationship or a straight relationship but instead should stay neutral. Instead, the argument should be that person A should be able to decide who visits them in the hospital, and where their social security money goes after they die, etc.
As far as discrimination, government should be in the business or protecting people's ability to say "I don't like that behavior" rather than forcing them to accept it or else.
Discriminating against someone because of how they were born should be illegal. Discriminating against someone because of what they do should be a protected right.